Three-dimensional funicular analysis of masonry vaults

•Presents three-dimensional extension of thrust line analysis for masonry.•Offers practical limit analysis approach for unreinforced masonry vaults.•Describes robust optimization algorithm to find best-fit thrust networks.•Identifies degrees of freedom of funicular networks with fixed plan geometry.•Provides admissible stress states and lower bound on geometric safety factor.

This paper introduces a new computational equilibrium analysis method for unreinforced masonry vaults, which extends Thrust Network Analysis using structural matrix analysis and efficient optimization strategies. By identifying independent states of equilibrium of funicular networks with any topology and fixed plan geometry, a robust and efficient solving algorithm is presented that allows practical limit analysis of (historic) masonry vaults with complex geometry under parallel loading conditions by fitting a provided geometrical target, e.g. the vault's mid surface. The presented framework can be seen as a strong foundation for practical equilibrium analysis of vaulted masonry.